Hypermatrix Algebra: Applications in Parallel Image Processing

A unique algebraic methodology is presented for implementing parallel tasks on multistage multidimensional architectures. Such architectures are motivated by the potential of digital optical and optoelectronic computing. Structured tasks can be decomposed from their initial algebraic casting and shown to match known canonical forms representing desirable computing structures such as 2D Omega processor. Algebraic manipulation of two-dimensional data structures—typical in image processing—requires more powerful operations than those afforded by classical matrix algebra. To this end, hypermatrix algebra provides a compact treatment of multidimensional objects and associated operations. Mappings of linear transformations are demonstrated including 2D Hadamard transformations, matrix rotations, and transposition.     

Hypermatrix oriented supernode amalgamation

In this paper, we introduce a supernode amalgamation algorithm which takes into account the characteristics of a hypermatrix data structure. The resulting frontal tree is then used to create a variable-sized partitioning of the hypermatrix. The sparse hypermatrix Cholesky factorization obtained runs slightly faster than the one which uses a fixed-sized partitioning. The algorithm also reduces data dependencies which limit exploitation of parallelism.

A Power Algebra for Theory Change

Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations of the conjunction and disjunction connectives of the underlying logic.     

条件事件代数研究综述

综述了条件事件代数理论的原理、主要性质和应用．条件事件代数是一门新兴的解决不确定性、概率性和模糊性推理问题的学科,是在确保规则概率与条件概率相容的前提下,把布尔代数上的逻辑运算推广到条件事件(规则)集合中得到的代数系统,目的是为智能系统中的条件推理建立一个数学基础．该文也对比条件事件代数更一般的逻辑系统——关联事件代数理论进行了介绍．     

Hypermatrix scheme for finite element systems on CDC STAR-100 computer

A study is made of the adaptation of the hypermatrix (block matrix) scheme for solving large systems of finite element equations to the CDC STAR-100 computer. Discussion is focused on the organization of the hypermatrix computation using Cholesky decomposition and the mode of storage of the different submatrices to take advantage of the STAR pipeline (streaming) capability. Consideration is also given to the associated data handling problems and the means of balancing the I/O and cpu times in the solution process. Numerical examples are presented showing anticipated gain in cpu speed over the CDC 6600 to be obtained by using the proposed algorithms on the STAR computer.     

类关系代数的OODB理论—关联代数的分析

ＯＯＤＢ是数据库研究的新领域。文中介绍了用于面向对象数据库查询语言原型的ＯＯＤＢ理论－与关系代数相似的关联代数。通过与关系代数的比较，分析其特点，说明其优越性。最后给出基于关联的查询形式。     

Boolean Algebra as a Fragment of the Theory of Boolean Toposes

Basic identities of Boolean algebra are considered, and their categorical analogs are proved.     

对代数观Rough集理论的信息观解释

Rough集理论的代数观点和信息论观点在不相客容决策表中的不等价性导致了这两种观点得出的结论不一致。我们研究了使这两种观点等价的条件,定义一种新的决策表信息熵计算方法,在此方法的基础上给出了Routh集理论代数观的一种新的信息观解释,并证明了这种新的信息观与代数观是等价的。新的信息观定义为寻找高效的知识约简算法奠定了基础。     

代数图论方法在并行处理中的应用研究

并行处理提高了计算机解决问题的运算速度,在当代计算机科学技术占有重要的地位。代数图论方法对于并行处理的研究起着重要作用。就并行互连网结构与负载平衡中使用的代数图论方法进行了阐述,说明了代数图论方法为更深一步地研究并行处理指明了方向。     

基于三方元代数理论的时序机最优全分解

本文基于三方元代数理论，提出了时序机最优全分解的思想。它可作为衡量全分解质量的标墙。     

Trajectory Tracking Control of a PVTOL Aircraft Based on Linear Algebra Theory

In this work, a trajectory tracking control design is proposed for the planar vertical takeoff and landing (PVTOL) aircraft using linear algebra theory. The resulting control law is implemented easily since the equation to be solved is not complex. The tracking is achieved providing convergence of the tracking errors to zero, and simulation results show the good performance of the proposed controller.     

离散事件动态系统的代数理论及其应用——现状与展望

确定性、无决策的离散事件动态系统(DEDS)可以表述为代数系Dioid上的线性模型并由此进行一些有效的分析。本文首先对Dioid理论做了简单介绍,综述了Dioid上发展起来的系统论及控制论的研究成果,对代数方法在计算机集成制造系统(CIMS)中的应用、现存问题和发展方向进行了探讨。     

OreintXA:一种有效的XQuery查询代数

XQuery是XML查询语言的推荐标准.现有的XQuery处理策略有两种方法,一种是基于核心语法一次一结点的方法,另一种是基于查询代数的一次一集合的方法.单独使用这两种方法都不能很好地处理XQuery查询.一方面,基于核心语法树的方法效率低,而且很难优化,而现有基于代数的方法又不能很好地满足XQuery的过程化查询语言的特性.描述了一个有效的XQuery代数系统--OrientXA.它是在总结现有的基于代数的XQuery查询工作、分析未解决的问题,并吸收了前述的两种策略的思想的基础上提出来的.它第一次提出了构造模式树的概念,其中的构造操作符能体现XQuery的灵活特征.由于操作符具有很强的表达能力,OrientXA能够表达W3C的用例和XMark测试集的所有查询.     

三值逻辑函数RDSOP形式的代数理论和T门实现

三值逻辑函数简化的不相交SOP(RDSOP)形式是一种很有用的代数形式,研究表明,它在T门网络的设计和化简方面有重要应用.利用三值格代数的基本运算和主要性质,讨论了三值函数RDSOP形式的代数理论和算法,并给出了应用实例.利用以三值T门网络可以实现任意三值逻辑函数的原理,提出了基于RDSOP形式的三值T门网络最小化设计的一种方法,并给出了实例.从给出的实例可以看出,该方法是有效且可行的.     

Banana Algebra: Compositional syntactic language extension

We propose an algebra of languages and transformations as a means of compositional syntactic language extension. The algebra provides a layer of high-level abstractions built on top of languages (captured by context-free grammars) and transformations (captured by constructive catamorphisms).     

Counting Paths: Nondeterminism as Linear Algebra

Nondeterminism is considered to be ignorance about the actual state transition sequence performed during a computation. The number of distinct potential paths from state i to j forms a matrix [nij]. The behavior of a nondeterministic program is defined to be this multiplicity matrix of the state transitions. The standard programming constructs have behaviors defined in terms of the behaviors of their constituents using matrix addition and multiplication only. The spectral radius of the matrix assigned to an iterating component characterizes its convergence. The spectral radius is shown to be either 0 or else ? 1. The program converges iff the spectral radius is zero, diverges deterministically iff the spectral radius is one, and has a proper nondeterministic divergence iff the spectral radius exceeds one. If the machine has an infinite number of states the characterization of convergence is given graph theoretically. The spectral radii of synchronous and interleaved parallel noncommunicating systems are easily computed in terms of the spectral radii of the components.